FYS3410 - Vår 2017 (Kondenserte fasers fysikk) · 3) + (0.5 to 2) at% Cr 2 O 3 -- Sapphire is transparent and colorless (E g > 3.1 eV) -- adding Cr 2 O 3: • alters the band gap

FYS3410 - Vår 2017 (Kondenserte fasers fysikk) http://www.uio.no/studier/emner/matnat/fys/FYS3410/v16/index.html

Pensum: Introduction to Solid State Physics

by Charles Kittel (Chapters 1-9, 11, 17, 18, 20)

Andrej Kuznetsov

delivery address: Department of Physics, PB 1048 Blindern, 0316 OSLO

Tel: +47-22857762,

e-post: [email protected]

visiting address: MiNaLab, Gaustadaleen 23a

http://www.uio.no/studier/emner/matnat/fys/FYS3410/v16/index.html

2017 FYS3410 Lectures and Exam (based on C.Kittel’s Introduction to SSP, Chapters 1-9, 11, 17,18,20)

Module I – Periodic Structures and Defects (Chapters 1-3, 20)

T 17/1 12-15 Introduction. Crystal bonding. Periodicity and lattices. Lattice planes and Miller indices. Reciprocal space. 3h

W 18/1 09-10 Bragg diffraction and Laue condition 1h

T 24/1 12-14 Ewald construction, interpretation of a diffraction experiment, Bragg planes and Brillouin zones 2h

W 25/1 08-10 Surfaces and interfaces. Elastic strain in crystals 2h

T 31/1 12-14 Point defects and atomic diffusion in crystals 2h

W 01/2 08-10 Summary of Module I 2h

Module II – Phonons (Chapters 4, 5, and 18 pp.557-561)

T 07/2 12-14 Vibrations in monoatomic and diatomic chains of atoms; examples of dispersion relations in 3D 2h

W 08/2 08-10 Periodic boundary conditions (Born – von Karman); phonons and its density of states (DOS) 2h

T 14/2 12-14 Effect of temperature - Planck distribution; lattice heat capacity: Dulong-Petit, Einstein, and Debye models 2h

W 15/2 08-10 Comparison of different lattice heat capacity models 2h

T 21/2 12-14 Thermal conductivity and thermal expansion 2h

W 22/2 08-10 Vibrational and thermal properties of nanostructures 2h

T 28/2 12-14 Summary of Module II 2h

Module III – Electrons (Chapters 6, 7, 11 - pp 315-317, 18 - pp.528-530, and Appendix D)

W 01/3 08-10 Free electron gas (FEG) versus free electron Fermi gas (FEFG) 2h

T 07/3 12-14 DOS of FEFG in 3D; Effect of temperature – Fermi-Dirac distribution; heat capacity of FEFG in 3D 2h

W 08/3 08-10 Transport properties of electrons electrons – examples for thermal, electric and magnetic fields 2h

T 14/3 12-14 DOS of FEFG in 2D - quantum wells 2h

W 15/3 08-10 DOS in 1D – quantum wires, and in 0D – quantum dots 2h

T 21/3 12-14 Origin of the band gap; Nearly free electron model 2h

W 22/3 08-10 Kronig-Penney model; Empty lattice approximation; Number of orbitals in a band 2h

T 28/3 12-14 no lecture

W 29/3 08-10 no lecture

T 4/4 12-14 Effective mass method 2h

W5/4 08-10 Summary of Module III 2h

Easter break

Module IV – Semiconductors and Metals (Chapters 8, 9 pp 223-231, and 17)

T 18/4 12-14 Fermi surfaces in metals; approaches for energy band calculations 2h

W 19/4 08-10 Effective mass method for calculating localized energy levels for defects in crystals 2h

T 25/4 12-14 Intrinsic and extrinsic electrons and holes in semiconductors; carrier statistics 2h

W 26/4 08-10 p-n junction and metal-semiconductor contact 2h

T 02/5 12-14 Optical properties of metals and semiconductors 2h

W 03/5 08-10 Optoelectronic device demonstrations with Randi Haakenaasen 2h

T 09/5 12-14 Summary of Module IV 2h

Summary and repetition

T 16/5 12-14 Repetition - the course in a nutshell 2h

Exam

Week 22 , June 1-2, your presence is required for 1 h – please book your time in advance

Optical properties of solids

• Recap of the hydrogen optical spectrum and optical process in solids

• Absorption and reflection of light in metals

• Light absorption semiconductors

• Photoluminecence: 3D versus 2D semiconductors

• Use of p-n junctions in optics: LEDs and solar cells






•Use of p-n junctions in optics: LEDs and solar cells

ENG2000: R.I. Hornsey Optic: 5

Absorption or emission due to excitation or relaxation of

the electrons in hydrogen atom

Light that can be detected by the human eye has

wavelengths in the range λ ~ 450nm to 650nm &

is called visible light:

• The human eye can detect light

of many different colors.

• Each color is detected with

different efficiency.

3.1eV 1.8eV

Spectral Response of Human Eyes

Eff

icie

ncy

, 100%

400nm 600nm 700nm 500nm

Chapter 21 -

• Incident light is reflected, absorbed, scattered, and/or

transmitted:

Light interactions with solids

• Optical classification of materials:

Transparent Translucent

Opaque

Incident: I0

Absorbed: IA

Transmitted: IT

Scattered: IS

Reflected: IR

Chapter 21 - 8

Light Absorption

e0IIT

The amount of light absorbed by a material is

calculated using Beer’s Law

= absorption coefficient, cm-1

= sample thickness, cm

= incident light intensity

= transmitted light intensity

0I

TI

ln

0I

IT

Rearranging and taking the natural log of both sides

of the equation leads to






• Use of p-n junction in optics: LEDs and solar cells

Chapter 21 -

• Absorption of photons by electron transitions:

• Unfilled electron states are adjacent to filled states

• Near-surface electrons absorb visible light.

Light absorption in metals

Energy of electron

Planck’s constant

(6.63 x 10-34 J/s)

freq. of incident light

filled states

unfilled states

DE = h required!

Chapter 21 - 11

Light reflection in metals

• Electron transition from an excited state produces a photon.

photon emitted

from metal

surface

Energy of electron

filled states

unfilled states

Electron transition

IR “conducting” electron

Chapter 21 - 12

• Reflectivity = IR /I0 is between 0.90 and 0.95.

• Metal surfaces appear shiny

• Most of absorbed light is reflected at the

same wavelength

• Small fraction of light may be absorbed

• Color of reflected light depends on

wavelength distribution

– Example: The metals copper and gold absorb light

in blue and green => reflected light has gold color

Light reflection in metals

Chapter 21 -






• Use of diodes in optics: LEDs and solar cells

Chapter 21 -

Absorption of light of frequency by by electron transition

occurs if h > Egap

• If Egap < 1.8 eV, all light absorbed; material is opaque (e.g., Si, GaAs)

• If Egap > 3.1 eV, no light absorption; material is transparent and

colorless (e.g., diamond)

Light absorption in semiconductors

• If 1.8 eV < Egap < 3.1 eV, partial light absorption; material is colored

blue light: h = 3.1 eV

red light: h = 1.8 eV

incident photon

energy h

Energy of electron

filled states

unfilled states

Egap

Examples of photon energies:

Chapter 21 -

Valence Band – Conduction Band Absorption

(Band to Band Absorption)

Conduction Band, EC

Valence Band, EV

Egap h = Ephoton

This process obviously requires that the minimum energy of a

photon to initiate an electron transition must satisfy

EC - EV = h = Egap

If h > Egap then obviously a transition

can happen. Electrons

are then excited to the

conduction band.

Chapter 21 - 16

Ge (min)hc

Eg (Ge)

(6.63 x 1034 J s)(3 x 108 m/s)

(0.67 eV)(1.60 x 1019 J/eV)

Computations of Minimum

Wavelength Absorbed

Note: the presence of donor and/or acceptor states allows for light

absorption at other wavelengths.

Solution:

(a) What is the minimum wavelength absorbed by

Ge, for which Eg = 0.67 eV?

Ge (min)1.86 x 10 -6 m 1.86m

(b) Redoing this computation for Si which has a band gap

of 1.1 eV

Si(min)1.13m

ENG2000: R.I. Hornsey Optic: 17

• Hence, the absorption coefficients of various

semiconductors look like:

Direct Indirect Band Gap Semiconductors

E

CB

k–k

Direct Bandgap

(a) GaAs

E

CB

VB

Indirect Bandgap, Eg

k–k

kcb

(b) Si

E

k–k

Phonon

(c) Si with a recombination center

Eg

Ec

Ev

Ec

Ev

kvb VB

CB

Er

Ec

Ev

Photon

VB

(a) In GaAs the minimum of the CB is directly above the maximum of the VB. GaAs istherefore a direct bandgap semiconductor. (b) In Si, the minimum of the CB is displaced fromthe maximum of the VB and Si is an indirect bandgap semiconductor. (c) Recombination ofan electron and a hole in Si involves a recombination center .

© 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Chapter 21 - 19

• Color determined by the distribution of wavelengths: -- transmitted light

-- re-emitted light from electron transitions

• Example 1: Cadmium Sulfide (CdS), Eg = 2.4 eV

-- absorbs higher energy visible light (blue, violet)

-- color results from red/orange/yellow light that is transmitted

Color of Nonmetals

• Example 2: Ruby = Sapphire (Al2O3) + (0.5 to 2) at% Cr2O3

-- Sapphire is transparent and

colorless (Eg > 3.1 eV)

-- adding Cr2O3 : • alters the band gap

• blue and orange/yellow/green

light is absorbed

• red light is transmitted

• Result: Ruby is deep

red in color

Adapted from Fig. 21.9, Callister & Rethwisch 8e.

(Fig. 21.9 adapted from "The Optical Properties of

Materials" by A. Javan, Scientific American, 1967.)

40

60

70

80

50

0.3 0.5 0.7 0.9

Tra

nsm

itta

nce (

%)

ruby

sapphire

wavelength, (= c/)(m)

Some of the many applications

– Emission:

light emitting diodes (LED) & Laser Diodes (LD)

– Absorption:

– Filtering: Sunglasses, ..

Si filters (transmission of infra red light with simultaneous

blocking of visible light)







Chapter 21 - 22

Photoluminescence

• Luminescence – reemission of light by a material

– Material absorbs light at one frequency and reemits it at another

(lower) frequency.

– Trapped (donor/acceptor) states introduced by impurities/defects

activator level

Valence band

Conduction band

trapped states Eg

Eemission

Multiple Quantum Wells (MQWs)

repetitions of

ZnO/ZnCdO/ZnO

1.5nm

Quantum properties electrons at the excited state

Bulk properties electrons at the ground state

hν

”blue shift”

Vishnukanthan, et.al Solar Energy, 106, 82(2014)

”blue shift”

PL: optical excitation and subsequent radiative carrier

recombination

Photoluminecence: 3D versus 2D semiconductors

Photoconductivity • Charge carriers (electrons or

holes or both) created in the

corresponding bands by

absorbed light can also

participate in current flow,

and thus should increase the

current for a given applied

voltage, i.e., the conductivity

increases

• This effect is called

Photoconductivity

• Want conductivity to be controlled by

light. So want few carriers in dark → A

semiconductor

• But want light to be absorbed, creating

photoelectrons

• → Band gap of intrinsic

photoconductors should be smaller than

the energy of the photons that are

absorbed







LEDs

From Light-Emitting Diodes, Fred Schubert

Chapter 21 - 27

Solar Cells

• Solar cell operation - incident photons generate elecron-hole pairs.

- internal p-n junction field drive the current

- current increases with light intensity.

n-type Si

p-type Si

p-n junction

light

+

-

+ + +

- - -

creation of

Electron-hole pair

Solar Cells

Conventional pyramid textures can be readily obtained via anisotropic etching of (100)-oriented c-Si in alkaline

solutions, which is widely used in c-Si PV cell manufacturing.

Y.Wang, L.Yang, Y. Liu, Z.X Mei, W.Chen, J. Li, H.L.Liang, A.Yu.Kuznetsov and X.L.Du

Scientific Reports 5, 10843 (2015)

Maskless inverted pyramid texturization of silicon

Conventional pyramid textures can be readily obtained via anisotropic etching of (100)-oriented c-Si in alkaline

solutions, which is widely used in c-Si PV cell manufacturing.

So-called inverted pyramid (IP) arrays, outperform conventional textures of their superior structure and light-

trapping characteristics

Inverted

pyramid







Documents

FYS3410 - Vår 2017 (Kondenserte fasers fysikk) · 3) + (0.5 to 2) at% Cr 2 O 3 -- Sapphire is transparent and colorless (E g > 3.1 eV) -- adding Cr 2 O 3: • alters the band gap